The present invention relates generally to tachometers commonly utilized in electronically controlled servo systems.
Tachometers typically generate a signal (i.e. voltage or frequency) which is substantially proportional to its input shaft rotational velocity. Tachometers are often utilized in electronically controlled servo systems, either as feedback transducers for velocity servomechanisms or as feedback transducers in derivative feedback compensators for position servomechanisms. Such servomechanisms, and their system applications are explained in considerable detail in a book entitled FEEDBACK AND CONTROL SYSTEMS by Di Stefano III, Stubberud and Williams, and published as one of Schaum's Outline Series in Engineering by the McGraw-Hill Book Company of New York.
Conventionally, tachometers include an armature rotating within a fixed permanent magnet field such that voltage generated as a back emf is extracted (i.e., sensed) via a commutator-brush assembly. Unfortunately, the commutator-brush assembly detracts from the performance of such a tachometer because of brush drag and electronic noise as well as other related hysteresis effects. Thus, brushless tachometers utilizing a rotating permanent magnet field and a fixed armature are often used in applications which mandate superior performance. Generally, brushless tachometers are considered superior to brush-type tachometers. However, because brushless tachometers typically have fewer armature windings, they often have greater output voltage ripple.
Accordingly, the present invention is a greatly simplified tachometer which has no armature and therefore no commutator-brush assembly nor solid state switching arrangement. The simplified tachometer is environmentally stable, has a substantially reduced output voltage ripple and can be constructed with extremely low values of rotational inertia if desired.
In general, the simplified tachometer of the present invention includes an eccentric or other sinusoidally undulating surface formed upon an input shaft whose rotational velocity is to be monitored. Proximity transducers are located within a housing in a quadrature arrangement. The proximity transducers are used to measure co-ordinate displacements x and y of the center of the eccentric with respect to the axis of rotation of the input shaft. The center of the eccentric is offset with respect to the axis of rotation of the input shaft by r, where r is equal to (y.sup.2 +x.sup.2).sup.0.5. Since rotational position .THETA. is equal to tan.sup.-1 (y/x), rotational velocity d.THETA./dt is equal to [1/(1+(y/x).sup.2)]d(y/x)/dt. This expression can be arithmetically simplified to d.THETA./dt=[x dy/dt-y dx/dt]/(Y.sup.2 +x.sup.2). Since r.sup.2 =(y.sup.2 +x.sup.2), this can be further simplified to d.THETA./dt=[x dy/dt-y dx/dt]/r.sup.2.
No further mathematical manipulation is required because both of the terms x dy/dt and y dx/dt are the product of two terms which preserve their algebraic signs. Thus, the entire expression is a "sign" and "magnitude" correct representation of the rotational speed of the input shaft.
In accordance with a second embodiment of the present invention, the improved tachometer employs a set of axially extending proximity transducers to measure similar coordinate displacements of a sinusoidally undulating surface. The sinusoidally undulating surface undulates with respect to a plane that is substantially orthogonal to the axial direction. In operation, the tachometer of the second preferred embodiment functions in substantially the same manner as the tachometer of the first embodiment described above.
In accordance with another principle feature of the present invention, "common mode" errors caused by transverse and/or axial movement of the input shaft are substantially eliminated by utilizing proximity transducers in arrangements which negate such common mode displacements. As described in a third structural embodiment, two sets of proximity transducers are disposed in an axial direction for measuring coordinate displacements of the sinusoidally undulating surface with respect to a plane that is substantially orthogonal to the axial direction. The two sets of transducers are positioned such that they are in an electronically opposed orientation (i.e., their output signals are 180 electrical degrees apart). Their combined output signals are summed algebraically by subtracting the output signals from one set from the output signals of the other set. Thus, any axial movement of the input shaft results in negligible modification to their combined output signals.
According to a fourth embodiment of the present invention, two sets of proximity transducers are disposed in radial directions for measuring coordinate displacements of a substantially cylindrical surface that undulates sinusoidally in a radial direction. The substantially cylindrical surface has at least two sinusoidal undulations (i.e., such that each proximity detector measures at least 720 electrical degrees per revolution of the input shaft). The two sets of transducers are positioned such that they are in an electronically synchronized orientation (i.e., their output signals are an integral multiple of 360 electrical degrees apart). Their combined output signals are summed algebraically by adding the output signals of one set to the output signals of the other set. Thus, any radial movement of the input shaft results in negligible modification to their combined output signals. In addition, since axial movement of the substantially cylindrical surface contributes only negligibly to the outputs of any of the proximity detectors, their combined output signals are substantially immune to axial "common mode" displacements as well.
In a fifth structural embodiment, three sets of proximity transducers are disposed in radial directions for measuring coordinate displacement of a substantially cylindrical surface which undulates sinusoidally in a radial direction. The substantially cylindrical surface has at least three sinusoidal undulations (i.e., such that each proximity detector measures 1080 electrical degrees per revolution of the input shaft). The three sets of transducers are positioned such that they are in an electronically synchronized orientation (i.e., their output signals are an integral multiple of 360 electrical degrees apart). Their combined output signals are manipulated trigonometrically and summed algebraically. Thus, any radial movement of the input shaft results in negligible modification to their combined output signals.
Various other objects and advantages of the present invention will become more apparent to one skilled in the art from reading the following specification taken in conjunction with the appended claims and the following drawings.